Math teacher seeking patterns.

Cartalk Puzzler: An Interesting Series of Numbers

When my kids were in school, they, like all the other kids I guess, had to learn their numbers. So each day for homework, they would bring home a list of numbers on a piece of paper, and they were asked to write out the letters that spelled that number, right next to each of them. So the number seven would be there, there’d be a blank space, the kids would have to write S – E – V – E – N. And of course they were also asked which numbers were spelled out by the various combinations of letters, so they’d see S – I – X – T – Y and write Sixty, etc.

One day, son number two presented me with a list of numbers and he said, “These numbers are different. There’s something special about them.” Here are the numbers:

Now there are no other numbers between one and a hundred inclusive that share this same characteristic. There’s something unusual about these numbers that son number two figured out. And I’ll give you an additional hint that order does not matter. The best hint is that he determined that these numbers should be on the list perhaps from his homework assignment.

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12 thoughts on “Cartalk Puzzler: An Interesting Series of Numbers”

Until “a hundred” I was leaning towards the number of letters in the written form being a factor of the named number. I can’t claim to have exhaustively checked all the other numbers in the 1-100 range, but the distribution of number-name lengths seems to point towards no.